Many known electronic calculators typically perform annuity calculations as if payments were due to be made at the end of each payment period. For example, such calculators typically perform future value (FV) and present value (PV) annuity calculations according to the following equations: ##EQU1## WHERE, PMT represents payment due at the end of each payment period,
i represents interest rate per compounding period, and PA1 n represents the number of compounding periods.
For certain types of transactions (e.g., loans, savings) where payments are due at the end of each payment period, such "end type" annuity calculations are proper. However, for other types of transactions (e.g., leases, insurance) where payments are typically due at the beginning of each payment period, such "end type" annuity calculations would be improper.
A prior-art electronic calculator of the type for performing annuity calculations with payments due at the end of each payment period is described, for example, in U.S. Pat. No. 3,863,060 entitled "General Purpose Calculator with Capacity for Performing Interdisciplinary Business Calculations", issued to France Rode, et al., Jan. 28, 1975. The above equations are shown in lines 61 and 62 of column 69 of said patent.
To utilize such a prior-art calculator for performing calculations when payments are due at the beginning of each payment period, it is often necessary for a user to manually substitute one value for another in the equation defining the calculation. For example, to calculate FV when payments are due at the beginning of each payment period, the user must manually substitute "PMT (1 + i)" for "PMT" in equation (1) above, prior to making the calculation. Likewise, to determine the values of other variables such as n, i, PMT or PV when payment is to be made at the beginning of each period rather than at the end of each period, the user must repeatedly perform the manual substitutions shown in Table 1 below each time such a determination is to be made.
TABLE 1 ______________________________________ SUBSTITUTION WHEN NECESSARY SOLVING FOR IN TERMS OF ______________________________________ PMT (1 + i) for PMT n (i, PMT, FV) or (i, PMT, PV) (n - 1) for n, and i n, PMT, PV (PV - PMT) for PV (n + 1) for n, and i n, PMT, FV (FV + PMT) for FV ##STR1## PMT n, i, PV ##STR2## PMT n, i, FV PMT (1 + i) for PMT PV n, i, PMT ______________________________________
to alleviate the inconvenience of repeated manual substitutions and the increased likelihood of user (operator) error that may be occasioned thereby, an electronic calculator is needed that is capable of performing annuity calculations automatically, i.e., without the need for manual entry of substituted data by an operator, when payments are due at the beginning of the payment period.